Identification of complex microbiological dynamic systems by nonlinear filtering

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Identification of complex microbiological dynamic systems by nonlinear filtering

Jean-Pierre Gauchi, Caroline Bidot, J.C. Augustin, Jean-Pierre Vila

To cite this version:

Jean-Pierre Gauchi, Caroline Bidot, J.C. Augustin, Jean-Pierre Vila. Identification of complex micro-

biological dynamic systems by nonlinear filtering. 6th. International Conference predictive Modeling

in Foods, Sep 2009, Washington, United States. �hal-02754475�

Table of Contents

Extended Abstracts 6

ICPMF

Technical Session 1

New Applications and Neural Networks - Part 1

1 General regression neural network model for growth of Salmonella serotypes on chicken skin for use in risk assessment

2 Design of challenge testing experiments to assess the variability of microbial behaviors in foods

3 Flexible querying of Web data for predictive modeling of risk in food

4 An integrated model for predictive microbiology and simultaneous

determination of lag phase duration and exponential growth rate. (not submitted) 5 An artificial neural networks approach for the rapid detection of the microbial spoilage of beef fillets based on Fourier Transform Infrared Spectroscopy data 6 Concept for the implementation of a generic model for remaining shelf life prediction in meat supply chains

Technical Session 2

Yeast, Mold and Spoilage Modeling

7 Modeling the effect of temperature and water activity on the growth boundaries of Byssochlamys fulva

8 Distributions of the germination time of Aspergillus flavus, Penicillium expansum and P. chrysogenum conidia depend on storage conditions (not submitted)

9 Modeling the growth/no growth interface of Zygosaccharomyces bailii in a

viscoelastic food model system

10 Development of a model describing the effect of temperature and (gel) structure on ochratoxin A production by Aspergillus carbonarius in liquid media and validation

11 The Quasi-Chemical Model to Saccharomyces cerevisiae in co-culture with Lactobacillus fermentum in sugar cane must (not submitted)

12 Development of a product specific model for spoilage of pasteurized fruit juices by Saccharomyces cerevisiae and validation under dynamic temperature conditions

Technical Session 3

Lag phase, growth and growth/no growth

13 Growth of Cronobacter spp. under dynamic temperature conditions occurring during cooling of reconstituted powdered infant formula (not submitted)

14 Modeling lag time of Bacillus cereus spore growth after heat treatment 15 Exploring lag phase and growth initiation of a yeast culture by means of an individual based model

16 Effects of temperature adaptation during growth or sporulation on heat resistance of Bacillus cereus spores

17 Comparative evaluation of growth/no growth interface of Listeria monocytogenes growing on stainless steel surfaces or in suspension, in response to pH and NaCl

18 Modeling the effect of acid and osmotic shifts from growth to no growth conditions and vice versa on the adaptation and growth of Listeria

monocytogenes

19 Individual cells lag time distributions of Enterobacter sakazakii

20 Studying the growth boundary and subsequent growth kinetics of Escherichia coli at different temperatures, pH and water activity levels

21 Prediction of time to growth of Bacillus cereus in egg as a function of

lysozyme, nisin and mild heat treatment.

Technical Session 4

Mechanistic Modeling and Systems Biology

22 Detection of a local contamination within a batch of food by random or systematic sampling (not submitted)

23 Assigning distributions representing variability and uncertainty to microbiological contamination data

24 Robustness analysis of an individual based model for microbial growth:

outcomes and insights

25 A hierarchal Bayesian model to estimate the growth of Listeria monocytogenes and natural flora in minced tuna

26 Identification of complex microbiological dynamic systems by nonlinear filtering

27 Modelling the influence of free fatty acids on heat resistance of Bacillus cereus spores

28 Effect of the growth environment on the strain variability of Salmonella enterica kinetic behavior (not submitted)

29 Predicting microbial inactivation and the correlating intracellular pH under salt and acid stress (not submitted)

Technical Session 5

Application of models to food commodities (e.g. seafood, meat, produce, beverages) - Part 1

30 Quantification of inhibition of Listeria monocytogenes by organic acids/pH relevant to semi-hard Dutch cheese (not submitted)

31 Modelling microbial competition in foods. Application to the behaviour of Listeria monocytogenes and lactic acid flora in diced bacon

32 Determination of the kinetic parameters for Campylobacter jejuni under

dynamic conditions. (not submitted)

33 Bayesian modelling of Clostridium perfringens growth in food products 34 Introducing a zero-modified negative binomial regression for estimating the effect of chilling on Escherichia coli counts from Irish beef carcasses

35 Use of fish shelf life prediction (FSLP) software for monitoring fresh turbot quality in the logistic chain

36 Probabilistic modeling of Listeria monocytogenes behaviour in diced bacon along the manufacture process chain

Technical Session 6

New Applications and Neural Networks - Part 2

37 The effect of singular and duplicate plating on the accuracy of estimating low numbers of micro-organisms in food (not submitted)

38 Estimating undetectably low post-pasteurization recontamination levels of milk with pathogens using surrogate microbial variables (not submitted)

39 Detection and identification of Acid-Lactic bacteria in an isolated system with near-infrared spectroscopy and multivariate regression modeling

40 Empirical meta-modelling of Salmonella Typhimurium at the farm level of the pork production chain

41 Application of network science to analyse the proteome of Escherichia coli during the lag phase under acid stress (not submitted)

42 Is the Bigelow z-concept consistent with non-log-linear inactivation models?

(not submitted)

43 Memory embedded structures of artificial neural networks: limitations and constraints in predictive modeling in foods

Technical Session 7

Application of models to food commodities (e.g. seafood, meat, produce, beverages) - Part 2

44 Development and validation of predictive models for the growth and survival

of Vibrio vulnificus in post harvest shellstock oysters

45 Development of predictive models for Listeria monocytogenes in selected refrigerated ready-to-eat foods

46 Modelling the kinetics of Listeria monocytogenes on frankfurters and other ready-to-eat meat products from manufacturing to consumption.

47 Predicting growth and growth boundary of Listeria monocytogenes-an international validation study with processed meat and seafood products

48 Predicting Staphylococcus aureus in the dairy chain

49 Introducing stochasticity in predictive modelling of Salmonella Typhimurium at the farm level of the pork production chain

50 The potential of end-products metabolites on predicting the shelf life of minced beef stored under aerobic and modified atmosphere with or without the effect of essential oils

Technical Session 8

Cross-Contamination; Microbial Competition Modeling; Model Performance and Validation - Miscellaneous

51 Risking more by modelling cocktail or strain?

52 Mathematical modeling the cross-contamination of food pathogens on the surface of ready-to-eat meats while slicing

53 Modelling the response of the kinetics of the arginine deaminase pathway of Lactobacillus sakei CTC 494 to acid stress

54 Comparison of two optical density methods and plate counts for growth parameter estimation (not submitted)

55 Relationship between cellular esterase activity and physiological state of stressed Listeria monocytogenes cells

Technical Session 9 Risk Assessment

56 Application of risk evaluation techniques to achieve a food safety objective for

Listeria monocytogenes and Salmonella spp. in a ready-to-eat meat

57 The use of meta-analytical tools in risk assessment modeling for food safety 58 A preliminary consumer risk assessment model of Salmonella in Irish pork sausages: transport and home refrigeration modules

59 Predictive microbiology models vs. modeling microbial growth within Listeria monocytogenes risk assessments: What gap? What impact?

60 Sensitivity analysis applied to a Listeria monocytogenes exposure assessment model

61 Developing a predictive model for quantifying the risk associated with in- factory Listeria monocytogenes recontamination and to identify suitable management options to reduce it.

62 Development of an online predictive modeling resource for food safety risk analysis decision making

63 Accounting for diversity of food borne pathogens. Cardinal growth parameters of the Bacillus cereus genetic groups and consequences for risk assessment 64 A mathematical risk model for Escherichia coli O157:H7 cross-contamination of lettuce during processing

65 Use of time temperature indicators as a risk management tool for Listeria monocytogenes in ready-to-eat foods (not submitted)

Technical Session 10

Non-Thermal and Thermal Inactivation

66 Application of QMRA to go beyond safe harbors in thermal processes. Part 1:

introduction and framework

67 Application of QMRA to go beyond safe harbors in thermal processes. Part 2:

quantification and examples

68 Quantification of the effect of culturing temperature on the salt-induced heat resistance of mesophilic and psychrotolerant Bacillus strains (not submitted) 69 Estimating probability of undetected failure of pasteurization process control using Fault Tree Analysis (not submitted)

70 microbiology approach for thermal inactivation of Hepatitis A Virus in acidified

berries

71 The Enhanced Quasi-chemical Kinetics Model for the Inactivation of Bacillus amyloliquefaciens by High Pressure Processing (HPP) (not submitted)

72 The effect of pre-acid shock in the induced heat resistance of Escherichia coli K12 at lethal temperatures

73 Modeling the combined effect of osmotic dehydration, nisin and modified atmosphere packaging on the shelf life of chilled gilthead seabream fillets (11) 74 Modelling the inactivation of Listeria monocytogenes and enzymes in mussel using high pressure processing (not submitted)

75 Application of kinetic models to describe heat inactivation of selected New Zealand isolates of Campylobacter jejuni (not submitted)

Technical Session 11

Applications of Predictive Modeling in Food Industry

76 Testing the Gamma hypothesis for two different hurdles, pH and

undissociated acid concentration, using Bacillus cereus F4810/72 (not submitted) 77 Development and use of Microbilogical spoilage models by the food industry (21)

78 Biological time temperature indicators as quality indicators of refrigerated products (34)

79 The importance of growth/no growth models for specific spoilage organisms within the food industry

80 SSSP version 3.1 from 2009: new freeware to predict growth of Listeria monocytogenes for a wide range of environmental conditions

81 Evaluation of the microbial growth for different transport conditions of warm raw pork carcasses

82 Monte Carlo simulation for the prediction of vitamin C and shelf-life of pasteurised orange juice (not submitted)

Posters

83 Predictive modelling of Escherichia coli O157:H7 cross contamination during

slaughter operations.

84 Evaluation of primary models to predict microbial growth by plate count and absorbance methods

85 A predictive model for the effect of temperature and water activity on the growth of pseudomonads in osmotically pretreated gilthead seabream fillets 86 Quantification of the effect of factors involved in challenge-test assays on the growth rate estimation of Listeria monocytogenes

87 Modeling chlorine resistance of Penicillium expansum in aqueous solutions (non submitted)

88 Predicting the growth of Salmonella enterica in fresh cilantro (not submitted) 89 Dynamic modelling of Listeria monocytogenes growth in vacuum packed cold smoked salmon. (not submitted)

90 Dynamic models for growth of Salmonella in ground beef and chicken at temperatures applicable to the cooking of meat.

91 Mathematical modeling for predicting the growth of Listeria monocytogenes during ripening and storage of Camembert type cheese (not submitted)

92 Using ComBase Predictor and Pathogen Modeling Program as support tools in outbreak investigation: an example from Denmark

93 Influence of sporulation conditions upon the heat resistance of Bacillius coagulans ATCC 7050 (not submitted)

94 Variability analysis of microbial inactivation after heat treatments and the survivor lag phase (not submitted)

95 Model for Listeria monocytogenes inactivation on dry cured ham by high hydrostatic pressure processing

96 Simulation of human exposure to mycotoxins in dairy milk

97 Predicting the lag phase of Listeria monocytogenes in fluctuating environmental conditions (not submitted)

98 Validation of predictive models for the growth and survival of total Vibrio parahaemolyticus in post harvest shellstock Asian oysters

99 Sampling plan optimisation: application to French diced bacon industry and

Listeria monocytogenes

100 Comparative modeling study of the effect of ozone flow rate and concentration on the colour degradation of orange juice.

101 Probability of survival and/or growth of Listeria monocytogenes cells exposed to heat-shock and essential oils treatments and proteomic analysis.

102 A predictive model for evaluating the effects of cultivation and farm-level processing on oat ß-glucan levels

103 A Weibull model to describe the effect of ethanol vapours on inactivation of dry harvested conidia of some Penicillium (not submitted)

104 A simple and economical dialysis method for modulation of water activity (not submitted)

105 Prediction of food spoilage by protease activity or lipase synthesis (not submitted)

106 Modelling growth of Penicillium expansum and Aspergillus niger under dynamic temperature conditions (not submitted)

107 Growth model of a Yersinia species in raw ground beef

108 Modelling the transport of Salmonella into whole-muscle meat products during marination and the subsequent lethality during thermal processing 109 Effect of the temperature on the inhibition of Escherichia coli and Listeria monocytogenes by lactic acid bacteria

110 Effects of citral, carvacrol and (E)-2-hexenal on growth inactivation of Listeria monocytogenes during heat treatment

111 Evaluation of growth boundary models - importance of data distribution and performance indices

112 Biological significance of predictive models for moulds (not submitted) 113 Validation of a predictive model for the effect of water activity and

temperature on growth of Botrytis cinerea and Penicillium expansum on table grapes (not submitted)

114 Predictive model for growth of Clostridium perfringens during cooling of

cooked uncured meat and poultry

115 Reconciliation of the population risk with the risk per serving in determining food safety objectives (not submitted)

116 Fatty acids composition of Polish commercial cakes as assessed by standard methods or by FT-IR spectroscopy

117 Modelling aspects of orange juice quality kinetics during ultrasound

processing

General regression neural network model for growth of Salmonella serotypes on chicken skin for use in risk assessment

T.P. Oscar

1 U.S. Department of Agriculture, Agricultural Research Service, Microbial Food Safety Research Unit, Room 2111, Center for Food Science and Technology, University of Maryland, Eastern Shore, Princess Anne, MD (thomas.oscar@ars.usda.gov)

Abstract

The objective of the present study was to develop a general regression neural network (GRNN) and Monte Carlo simulation model for growth of Salmonella on chicken skin with native flora and as a function of serotype, temperature and time for use in risk assessment.

Poultry isolates of Salmonella with natural resistance to antibiotics were used to investigate and model growth from a low initial dose (0.78 to 0.95 logs) on chicken skin with native flora. Computer spreadsheet and spreadsheet add-in programs were used to develop and simulate a GRNN model. Model performance was evaluated by determining the percentage of residuals in an acceptable prediction zone from -1 log (fail-safe) to 0.5 logs (fail- dangerous). The GRNN model had an acceptable prediction rate of 92% for dependent data (n = 464) and an acceptable prediction rate of 89% for independent data (n = 116), which exceeded the performance criterion for model validation of 70% acceptable predictions.

Differences among serotypes were observed with Kentucky exhibiting less growth than Typhimurium and Hadar, which had similar growth. Temperature abuse scenarios were simulated to demonstrate how the GRNN model can be integrated with risk assessment.

Keywords

Risk assessment, neural network, Monte Carlo simulation, predictive model, Salmonella, growth, chicken skin, strain variation.

Introduction

Salmonella are a leading cause of gastroenteritis and are often isolated from poultry (Bryan and Doyle 1995). There are over 2,300 serotypes of Salmonella yet only about 50 are responsible for most cases of gastroenteritis (Foley et al. 2008). The top three serotypes isolated from chickens are Enteritidis, Kentucky and Typhimurium. Variation of growth among serotypes of Salmonella has been observed (Fehlhaber and Kruger 1998; Oscar 1998).

However, whether growth of Kentucky differs from other serotypes of Salmonella has not been reported. Performance of predictive models can be improved by using better-fitting models. It has been reported that general regression neural network (GRNN) models outperform regression models and other types of neural network models in predictive microbiology applications (Jeyamkondan et al. 2001; Palanichamy et al. 2008). With the advent of commercial software applications that perform GRNN modelling, it is now easy to use GRNN modelling in predictive microbiology studies. Moreover, GRNN modelling software is compatible with Monte Carlo simulation software. Thus, it is possible to create GRNN models that use Monte Carlo simulation to model uncertainty and variability of independent variables. Output distributions from such models can be used in risk assessment.

The objective of the present study was to develop a GRNN model that employs Monte Carlo simulation to provide stochastic predictions of Salmonella growth from a low initial dose on raw chicken skin with native flora as a function of serotype (Typhimurium, Kentucky, Hadar), temperature (5 to 50C) and time (0 to 8 h) for use in risk assessment.

Materials and Methods

Isolates of Salmonella serotypes Typhimurium, Kentucky, and Hadar were obtained from

poultry. Typhimurium was resistant to chloramphenicol (C), ampicillin (A), tetracycline (T)

and streptomycin (S). Kentucky was resistant to novobiocin (N), A, T and S. Hadar was

resistant to T, sulfasoxazole (U), gentamicin (G), and S. Xylose lysine tergitol 4 base agar medium without tergitol (XL) but supplemented with 25 mM HEPES (H) and 25 g per ml of C, A, T, S, N, U or G was used for enumeration. A full 3 x 10 x 5 x 2 x 2 factorial arrangement of serotype (Typhimurium, Kentucky, Hadar), temperature (5, 10, 15, 20, 25, 30, 35, 40, 45, 50C), time (0, 2, 4, 6, 8 h), trial (1, 2), and sample (a, b) was used for model development. Replicate trials were conducted in separate weeks with different batches of chicken skin. Chicken thigh skin portions (~0.25 g) were spot inoculated (5 l) with an initial log number of 0.95 for Typhimurium, 0.78 for Kentucky and 0.91 for Hadar. Pulsified samples (skin portion + 9 ml buffered peptone water; BPW) were used for enumeration. A combination three-tube MPN and spiral plating method with XLH-CATS for Typhimurium, XLH-NATS for Kentucky, and XLH-TUGS for Hadar was used for Salmonella enumeration (Oscar 2006). A dataset was created in an Exel spreadsheet with separate columns for serotype (independent categorical variable), temperature (independent numerical variable), time (independent numerical variable) and log number (dependent variable). A GRNN model was trained by the method of Specht (1991) using Neural Tools software. Eighty percent of data were used for training and 20% were used for testing. Percentage of residuals in an acceptable prediction zone from -1 log (‘fail-safe’) to 0.5 logs (‘fail-dangerous’) with an acceptable prediction rate criterion of 70% was used for model validation (Oscar 2006). A discrete distribution was used to model serotype prevalence, whereas pert distributions were used to model temperatures and times of abuse. The GRNN model was simulated with @Risk settings of Latin Hypercube sampling, 10

iterations, and a correlation between temperature and time of 0 or -1. The best-fitting distributions for output data (log change) were determined using the Chi-square statistic within the BestFit function of @Risk.

5 10 15 20 25 30 35 40 45 50

-2 -1 0 1 2

Hadar Typhimurium Kentucky A) Train (n = 464)

0 2 4 6 80 2 4 6

80 2 4 6 80 2 4 6

80 2 4 6 80 2 4 6

80 2 4 6 80 2 4 6

80 2 4 6 80 2 4 6

8 hC Independent variables

Residual (log)

5 10 15 20 25 30 35 40 45 50

-2 -1 0 1 2

Hadar B) Test (n = 116)

Typhimurium Kentucky

0 2 4 680 2 4 680 2 4 680 2 4 680 2 4 680 2 4 680 2 4 680 2 4 680 2 4 680 2 4 68

C

h

Independent variables

Residual (log)

Figure 1. Residual plots for A) dependent data for training and B) independent data for testing model performance. Residuals were sorted by temperature and then time in ascending order. Major ticks correspond to temperature and 8 h of incubation whereas minor ticks to the left of major ticks correspond to incubation times of 0, 2, 4 and 6 h, respectively, for the temperature indicated on the major tick. Lower and upper dashed lines are boundaries of the acceptable prediction zone.

Results

The GRNN model was trained on 464 data points and had an acceptable prediction rate of

91.8%. There were no signs of systematic prediction bias as a function of serotype,

temperature or time (Figure 1a). When tested against independent data (n = 116; Figure 1b),

the GRNN model had an acceptable prediction rate of 88.8% and did not exhibit systematic

prediction bias as a function of independent variables. Thus, the model was validated because

its acceptable prediction rates for dependent and independent data exceeded 70%.

0 1 2 3 4 5 6 7 8 0

1 2 3 4 5 6

Typhimurium Kentucky Hadar A) 37C

Time (h)

Salmonella (log)

5 10 15 20 25 30 35 40 45 50

0 1 2 3 4 5 6

Typhimurium Kentucky Hadar B) 5.3 h

Temperature (C)

Salmonella (log)

Figure 2. Output graphs from the general regression neural network model for growth of Salmonella on raw chicken skin as a function of A) time at 37



The GRNN model predicted the log number of Salmonella for temperatures and times that were and were not investigated but that were within ranges of independent variables used in model development (e.g. Figure 2). Overall, Kentucky exhibited less growth than Typhimurium and Hadar, which had similar growth on raw chicken skin with native flora.

-1 0 1 2 3 4 5

0 1 2 3

4 A) RiskPearson5(4.4594,1.5797,RiskShift(-0.26825))

Output data Distribution fit

Log change

Frequency

-1 0 1 2 3 4 5

0 2 4 6 8 10

Output data Distribution fit B) RiskLogistic(0.047094,0.056875)

Log change

Frequency

Correlation = 0 Correlation = -1

Figure 3. Output data and best-fit distributions from the general regression neural network and Monte Carlo simulation model for growth of Salmonella on raw chicken skin.

Temperature abuse scenarios were simulated to demonstrate how the GRNN model can be integrated with risk assessment. Examples of output distributions from the GRNN model that can be used as input distributions in a risk assessment model are shown in Figure 3.

Discussion

Accurate and unbiased predictions of pathogen growth are needed to safeguard public health.

Models that under-predict pathogen growth result in consumption of unsafe food, whereas

models that over-predict pathogen growth result in destruction of safe food, which is not

desirable. Most studies in predictive microbiology use a mixture of pathogen strains for

model development. The idea is that this will result in a ‘fail-safe’ model because the fastest-

growing strain will predominate under the conditions tested. However, models developed

with a cocktail of strains could be overly ‘fail-safe’. For example, if the current model had

been developed with a cocktail of Typhimurium, Kentucky and Hadar, the faster-growing

serotypes Typhimurium and Hadar would have predominated and the resulting model would

have over-predicted growth of Salmonella on raw chicken skin contaminated with the slower-

growing serotype Kentucky. Thus, by developing models with individual strains and then

modelling growth as a function of serotype prevalence, more accurate predictions are

obtained.

Models in predictive microbiology are usually developed in three stages (primary, secondary and tertiary) using regression methods. Limitations of this approach are that it is time consuming, requires significant training in regression analysis and uses regression models that are inflexible. Neural network modelling overcomes limitations of regression modelling as it is fast, requires only a basic understanding of the method, is flexible and outperforms regression modelling in predictive microbiology applications (Garcia-Gimeno et al. 2003;

Hajmeer et al. 1997; Jeyamkondan et al. 2001; Palanichamy et al. 2008). The latter studies all used regression for primary modelling and neural networks for secondary modelling. In the present study, a general regression neural network was used in one-step for primary, secondary and tertiary modelling and the resulting model had acceptable and high performance (ca. 90% acceptable predictions). Thus, it does not seem necessary to use regression modelling in tandem with neural network modelling when neural network modelling is capable of developing predictive models in one-step at a considerable savings in time, effort and performance.

Risk assessment provides stochastic predictions of the risk of adverse health outcomes from food produced by different farm-to-table scenarios. Predictive models are used in risk assessment to provide stochastic predictions for individual pathogen events, such as growth.

Consequently, the GRNN model developed in this study was configured for risk assessment by using Monte Carlo simulation in tandem with GRNN modelling software to provide stochastic predictions of Salmonella growth.

Conclusions

In the current study, a GRNN and Monte Carlo simulation model was developed and validated for making stochastic predictions of Salmonella growth from a low initial dose on raw chicken skin as a function of serotype, temperature and time and thus, the models’

predictions can be used with confidence in risk assessment. However, because parameters of the GRNN model are not provided by the commercial software application, deployment of the model might be limited by the requirement that users possess the commercial software used to run and simulate the model and make predictions.

Acknowledgements

The author appreciates the outstanding assistance of Jacquelyn Ludwig (Agricultural Research Service) and Celia Whyte and Olabimpe Olojo (University of Maryland, Eastern Shore).

References

Bryan,F.L. and Doyle,M.P. (1995) Health risks and consequences of Salmonella and Campylobacter jejuni in raw poultry. Journal of Food Protection, 58, 326-344.

Fehlhaber,F. and Kruger,G. (1998) The study of Salmonella enteritidis growth kinetics using Rapid Automated Bacterial Impedance Technique. J.Appl.Microbiol., 84, 945-949.

Foley,S.L., Lynne,A.M. and Nayak,R. (2008) Salmonella challenges: prevalence in swine and poultry and potential pathogenicity of such isolates. J.Anim Sci., 86, E149-E162.

Garcia-Gimeno,R.M., Hervas-Martinez,C., Barco-Alcala,E., Zurera-Cosano,G. and Sanz-Tapia,E. (2003) An artificial neural network approach to Escherichia coli O157:H7 growth estimation. Journal of Food Science, 68, 639-645.

Hajmeer,M.N., Basheer,I.A. and Najjar,Y.M. (1997) Computational neural networks for predictive microbiology II. Application to microbial growth. International Journal of Food Microbiology, 34, 51-66.

Jeyamkondan,S., Jayas,D.S. and Holley,R.A. (2001) Microbial growth modelling with artificial neural networks.

International Journal of Food Microbiology, 64, 343-354.

Oscar,T.P. (1998) Growth kinetics of Salmonella isolates in a laboratory medium as affected by isolate and holding temperature. Journal of Food Protection, 61, 964-968.

Oscar,T.P. (2006) Validation of a tertiary model for predicting variation of Salmonella Typhimurium DT104 (ATCC 700408) growth from a low initial density on ground chicken breast meat with a competitive microflora. Journal of Food Protection, 69, 2048-2057.

Palanichamy,A., Jayas,D.S. and Holley,R.A. (2008) Predicting survival of Escherichia coli O157:H7 in dry fermented sausage using artificial neural networks. Journal of Food Protection, 71, 6-12.

Specht,D.F. (1991) A general regression neural network. IEEE Trans.Neural.Netw., 2, 568-576.

Design of challenge testing experiments to assess the variability of microbial behaviors in foods

J.-C. Augustin

, H. Bergis

, G. Bourdin

, M. Cornu

, O. Couvert

, C. Denis

, V.

Huchet

, S. Lemonnier

, A. Pinon

, M. Vialette

, V. Zuliani

and V. Stahl

1 Unité MASQ, Ecole Nationale Vétérinaire d’Alfort, 7 Avenue du Général de Gaulle – F-94704 Maisons-Alfort Cedex, France (jcaugustin@vet-alfort.fr)

2 Microbiologie quantitative et estimation des risques (MQER), Agence française de sécurité sanitaire des aliments (Afssa), 23 avenue du Général de Gaulle – F-94706 Maisons-Alfort Cedex, France (m.simon-cornu@afssa.fr)

3 Agence française de sécurité sanitaire des aliments (Afssa), LERPPE, rue Huret Lagache – F-62200 Boulogne Sur Mer, France (g.bourdin@boulogne.afssa.fr)

4 Cellule opérationnelle Sym’Previus, ADRIA Développement, Creac’h Gwen, F-29196 Quimper Cedex, France (olivier.couvert@adria.tm.fr)

5 ADRIA Normandie, boulevard du 13 juin 1944, F-14310 Villers-Bocage, France (cdenis@adrianie.org)

6 ADRIA Développement, Creac’h Gwen, F-29196 Quimper Cedex, France (veronique.huchet@adria.tm.fr)

7 Institut Pasteur de Lille, 1 rue du Professeur Calmette, BP 245, F-59019 Lille Cedex, France (anthony.pinon@pasteur-lille.fr)

8 Ifip Institut du porc, 7 avenue du Général de Gaulle, F-94704 Maisons-Alfort Cedex, France (veronique.zuliani@ifip.asso.fr)

9 Aérial, Parc d'Innovation, F-67412 Illkirch, France (v.stahl@aerial-crt.com)

Abstract

The assessment of the evolution of microorganisms naturally contaminating food must take into account the variability of biological factors, food characteristics and storage conditions.

A research project involving eight French laboratories was conducted to quantify the variability of growth parameters of Listeria monocytogenes obtained by challenge testing in five foods. The residual variability corresponded to a coefficient of variation (CV) of approximately 20% for the growth rate (µ

) and 120% for the parameter K (=µ

.lag time).

The between batches and between manufacturers variability was very dependent on the food tested and the CV of µ

ranged from 0 to 80%. The initial physiological state variability led to a CV of 110% for the factor K. It appeared that repeating a limited number of challenge tests in different batches/manufacturers for different initial physiological states is often sufficient to assess the variability of the behavior of L. monocytogenes in a given food.

Keywords

Exposure assessment, biological variability, challenge testing, Listeria monocytogenes Introduction

The assessment of the evolution of microorganisms that naturally contaminate food must take

into account the variability of factors influencing the microbial behavior, i.e., biological

factors, physico-chemical and microbial food characteristics, and storage conditions. The

probabilistic software developed in the Sym’Previus project was designed to easily perform

microbial exposure assessment and to combine the different source of variability with primary

and secondary predictive microbiology models (Couvert et al., 2007). The biological

variability of bacterial cardinal values is already set in the software but the variability of

growth parameters, initial contamination, food characteristics and storage conditions must be

specified by the users. It is really challenging to specify the variability of maximum growth

rate and lag time of naturally contaminating microorganisms. The estimation of these

parameters in natural conditions of contamination is generally impossible for pathogenic

microorganisms and operators must usually perform challenge testing. A research project

involving eight French laboratories was conducted to quantify the variability of growth

parameters of L. monocytogenes obtained by challenge testing in five different foods. The

objective was to evaluate the impact of within and between batches variability, between

manufacturers variability, and microbial initial physiological state variability, on the

variability of the growth parameters to optimize the challenge testing methodology applied when evaluating the variability of the behavior of microorganisms in foods.

Materials and Methods

The following foods were studied: i) pâté from one batch, ii) smoked herring from four batches of two manufacturers, iii) cooked ham from seven batches and three manufacturers, iv) cooked chicken belonging to two batches of one manufacturer, and v) surimi salad from different batches of one manufacturer.

Each food was studied by two or three laboratories and was artificially contaminated with exponentially growing or starved cells of one strain of L. monocytogenes in order to evaluate the impact of physiological state on the growth parameters. Contaminated food samples were stored at 8°C and enumerations of L. monocyotgenes were performed on three samples at approximately 10 different times during the lag, the exponential and the stationary phases of the growth curve. Some experiments were replicated with the same batch of food, the same physiological state and the same laboratory to estimate the residual variability of growth parameters. pH and water activity (a

) of foods were measured by laboratories to characterize the variability of physico-chemical characteristics of studied foods.

The maximum specific growth rate ( µ

) and the lag time (lag) were estimated for each growth curve by fitting the logistic with delay growth model (Pinon et al., 2004). In a second time, the variability of µ

and of the product K= µ

.lag representing the initial physiological state of contaminating cells was analyzed in order to determine the impact of the studied factors. Growth simulations were performed with the probabilistic software of Sym’Previus to combine the different variability sources in order to predict the growth curves of L. monocyotgenes or the probabilities to exceed given concentrations in foods.

Results and Discussion

The residual variability of µ

was almost constant and a coefficient of variation (CV) of 20% was observed on average (Table 1). This variability was not explained by the variability of measured physico-chemical parameters since simulations performed for the species L.

monocytogenes (12 strains) by only taking into account the observed variability of pH and aw of studied foods generated less variability for µ

than the observed one (Table 1). This variability could then be linked to the variability of other not measured food characteristics or to the measurement uncertainty of µ

when performing challenge testing. This result is not surprising since Baranyi and Roberts (1995) described repeatability standard errors of approximately 10% of the estimated growth rate in synthetic media. On the contrary, the residual variability of K was more pronounced and more variable with a mean CV of 120%

(Table 1). This great variability of K can be easily explained by the difficulty for laboratories to experimentally reproduce specific bacterial physiological states. Since the residual variability of µ

and K was relatively large, no significant effect of the laboratory performing the challenge test was observed for these two parameters.

The between batches and manufacturers effects on µ

were very variables with CV ranging from 0 to 23% and from 0 to 81%, respectively (Table 1). The variability of K linked to the initial physiological state was relatively constant, which is consistent with the fact that only two physiological states were studied, and the CV was 110% on average.

The growth curves of L. monocytogenes generated for each food taking into account the

biological variability, the variability of food characteristics and the variability of growth

parameters summing the means of residual, between batches, between manufacturers and

physiological state variances are shown in Figure 1. For pâté we observed that, the mean

residual variability of K being larger than the observed one, the lag time was sometimes

overestimated but the predicted behavior was relevant on the whole. For smoked herring, the

mean between manufacturers variability lead to an overestimation of the observed variability

while for the cooked ham, this mean variability was not sufficient to describe the observed

one.

Table 1. Variability sources for growth parameters of L. monocytogenes.

µ

Food

pH (mean±SD)

a_w (mean±SD)

Variability (CV%)

Physico- chemical

characteristics Residual Batch Manu-

facturer Residual Physio-

logical state

Input _ 16 ND* ND 44 115

Pâté 5.94±0.10 0.976±0.004

Output 9 17 _ _ _ _

Input _ 19 23 0 103 ND

Smoked

herring 6.37±0.08 0.966±0.009

Output 26 32 40 40 _ _

Input _ 20 0 81 135 103

Cooked

ham 6.08±0.07 0.975±0.007

Output 15 25 25 75 _ _

Input _ 22 17 ND 141 88

Cooked

chicken 6.30±0.19 0.974±0.008

Output 17 23 29 _ _ _

Input _ 21 0 ND 196 137

Surimi

salad 6.30±0.25 0.984±0.010

Output 17 26 26 _ _ _

Mean input 20 10 41 124 111

* ND not determined.

It seems thus that the residual variability of 20% for µ

and 120% for K can be used to describe the variability of growth parameters for a given batch and a given physiological state but these parameters are too much varying for between batches and between manufacturers variability. Their impact on growth parameters is thus difficult to predict and several challenge tests are need. Furthermore it is hazardous to set the expected values of growth parameters with only one challenge test.

Figure 1. Observed (

) and simulated (95% confidence bands) growth of L. monocytogenes at

8°C in (a) pâté, (b) smoked herring, (c) cooked ham, and (d) surimi salad.

Then we proposed to perform three different challenge tests to estimate the expected values and standard deviations of µ

and K. Depending on the studied factors influencing the growth, the challenge tests can be performed with three different batches or manufacturers and with three different physiological states. The Table 2 reports the results obtained when comparing this approach with the one consisting to use only one challenge test and fixing theoretical variances. The typical prediction errors (MARE) when predicting the probability to exceed a given concentration were lower when three challenge tests were performed and the dispersions of the relative errors (SDRE) were also lower.

Table 2. Mean absolute relative errors (MARE) and standard deviations of relative errors (SDRE) for predictions of probabilities P to exceed given concentrations of L. monocytogenes

in foods stored at 8°C. The reference probabilities are those obtained by using all the challenge tests performed.

1 kinetic 3 kinetics

Food Variability sources MARE (%) SDRE (%) MARE (%) SDRE (%) Pâté

(P>7 log cfu/g 8 days) residual 99 135 60 71

Smoked herring (P>6 log cfu/g 15 days)

residual, batch,

manufacturer 63 86 42 41

Cooked ham

(P>6 log cfu/g 10 days)

residual, batch, manufacturer, physiological state

126 154 35 20

Cooked chicken (P>6 log cfu/g 8 days)

residual, batch,

physiological state 55 67 24 14

Surimi salad

(P>7 log cfu/g 10 days)

residual, batch,

physiological state 37 43 4 _

Conclusion

The implementation of challenge tests to assess the variability of the growth parameters of foodborne pathogens is a keystone because the impact of the different sources of variability is unpredictable. By reproducing challenge tests in three different conditions it seems possible to satisfactorily evaluate the impact of between batches, between manufacturers and initial physiological state on growth parameters.

Acknowledgements

This work is part of the national research program ACTIA 05.9 and was supported by a grant from ACTIA, the French Ministry of Agriculture and food business operators. This project is part of the National French Technological Network (RMT) “Expertise on determination of food products microbial shelf-life”.

References

Baranyi J. and Roberts T.A. (1995) Mathematics of predictive food microbiology. International Journal of Food Microbiology 26, 199-218.

Couvert O., Augustin J.-C., Buche P., Carlin F., Coroller L., Denis C., Jamet E., Mettler E., Pinon A., Postollec F., Stahl V., Zuliani1 V. and Thuault D. (2007) Optimising food process and formulation through Sym’Previus..

5^th International Conference Predictive Modelling in Foods, September 16-19, 2007, Athens, Greece.

Pinon A., Zwietering M., Perrier L., Membré J.-M., Leporq B., Mettler E., Thuault D., Coroller L., Stahl V. and Vialette M. (2004) Development and validation of experimental protocols for use of cardinal models for prediction of microorganism growth in food products. Applied and Environmental Microbiology 70, 1081–

1087.

Flexible querying of Web data for predictive modelling of risk in food P. Buche

, O. Couvert

, J. Dibie-Barthélemy

, E. Mettler

, L. Soler

1INRA, UP 1204 Méthodologies d’analyse du risque alimentaire, F-75005 Paris, France (buche@paris.inra.fr, dibie@agroparistech.fr, lsoler@paris.inra.fr)

2AgroParisTech, UP 1204 Méthodologies d’analyse du risque alimentaire, F-75005 Paris, France

3ADRIA Développement, Creac’h Gwen, 29196 Quimper Cedex, France (olivier.couvert@adria.tm.fr)

4Soredab (Groupe SOPARIND BONGRAIN), La Tremblaye, 78125 La Boissière-Ecole, France (eric.mettler@soredab.org)

Abstract

A preliminary step to risk in food assessment is the gathering of experimental data. In the framework of the Sym’Previus project, we have designed a complete data integration system opened on the Web which allows a local database to be complemented by data extracted from the Web and annotated using a domain ontology. We propose in this paper a flexible querying system using the domain ontology to scan simultaneously local and Web data in order to feed the predictive modelling tools available on the Sym’Previus platform. Special attention is paid on the way fuzzy annotations associated with Web data are taken into account in the querying process, which is an important originality of the proposed system.

Keywords

Web data, flexible querying, ontology, predictive microbiology Introduction

A preliminary step to risk in food assessment is the gathering of experimental data (Tamplin et al. 2003, Baranyi and Tamplin 2004, McMeekin et al. 2006). In the framework of the Sym’Previus project (Couvert et al 2007 and http://www.symprevius.org), we have designed a complete data integration system opened on the Web which allows a local database (Buche et al. 2005) to be complemented by data extracted from the Web (Hignette et al. 2008). The local data were classified by means of a predefined vocabulary organized in taxonomy, called ontology, which is also used to extract pertinent data from the Web. Our aim is to integrate the data found on the Web with the local data by means of a flexible querying system which allows the end-user to retrieve the nearest local and Web data corresponding to his/her selection criteria. Our solution allows the end-user to query simultaneously and uniformly local and Web data in order to feed the predictive modelling tools available on the Sym’Previus platform. We first remind the semi-automatic annotation method (implemented in the @WEB tool, see @Web demo) which allows data to be retrieved from data tables found in scientific documents on the Web and to be annotated thanks to the domain ontology.

Second, we present the original contribution of the paper, which consists in the design of the flexible querying system, called MIEL++, which permits to query simultaneously the local data and the semantic annotated Web data, in a transparent way to the end-user, thanks to the ontology. This system is flexible because (i) it allows the end-user to express preferences in his/her selection criteria and (ii) it takes into account, in the answers building, the different kinds of fuzziness of the semantic annotated Web data. This second point is essential to deal with the uncertainty of the Web data and with the imperfection of their annotations.

Materials and Methods

The semi-automatic annotation method

Web data have been semi-automatically classified by means of a predefined vocabulary,

called ontology. This ontology is composed of data types meaningful in the domain of risk in

food and semantic relations linking those data types. Data types are described in two different

ways depending on whether their associated values are symbolic (Food product,

Microorganism …) or numeric (Temperature, Time …). Symbolic types are described by

taxonomies of possible values (for example, a taxonomy of microorganisms). Numeric types are described by their possible set of units (for example, °C or °F for Temperature, but no unit for pH or a

), and their possible numerical range (for example, [0, 14] for pH). Semantic relations are defined by a result data type and a set of access types. For example, the relation GrowthParameterAw, representing the growth limits of a micro-organism for any food product, has for access type the symbolic type Microorganism and for result types the numeric type a

. Our annotation algorithm first annotates the symbolic columns and the numeric columns and then uses these annotations to determine the semantic relations present in the Web table (see Hignette et al. 2008 for more details). Figure 1 shows a part of the RDF graph which represents the annotations associated with the first line of Table 1 extracted from the Web. RDF (Resource Description Framework) is the language recommended by the W3C (World Wide Web consortium) to represent semantic annotations associated with Web resources. A particularity of our RDF annotations is to propose an explicit representation (1) of the similarity between terms of the ontology and terms of the Web and (2) of the imprecision of numerical data, using a homogeneous framework, the fuzzy set theory.

Table 1: Cardinal values.

Organism Aw minimum Aw optimum Aw maximum

Clostridium 0.943 0.95-0.96 0.97

Staphylococcus 0.88 0.98 0.99

Salmonella 0.94 0.99 0.991

Figure 1: Annotations associated by our algorithm to the first line of Table 1

In Figure 1, the RDF annotation expresses that the row (having the identifier uriRow1 in the RDF graph) is annotated by a discrete fuzzy set, called DFSR1. This fuzzy set has a semantic of similarity and indicates the list of closest relations of the ontology recognized in the first row. Only the relation GrowthParameterAw belongs to this fuzzy set with the pertinence score of 1.0 which expresses the degree of certainty associated with the relation recognition by our semantic annotation process. The access type of the relation, which is an instance of the symbolic type Microorganism, is annotated by a discrete fuzzy set, called DFS1. This fuzzy set has a semantic of similarity and indicates the list of closest terms of the ontology compared to the term Clostridium. Two terms (Clostridium Perfringens and Clostridium Botulinum) belong to this fuzzy set with a membership degree of 0.5. The result type of the relation, which is an instance of the numeric type aw, is annotated by a continuous fuzzy set, called CFS1. This fuzzy set has a semantic of imprecision and indicates the possible growth limits ([0.943, 0.97]) and the possible optimal growth limits ([0.95, 0.96]).

Design of the flexible querying system MIEL++

The MIEL++ querying system relies on the domain ontology used to index the local data and

to annotate the Web data. MIEL++ allows the end-user to retrieve the nearest local and Web

data corresponding to his/her selection criteria expressed as fuzzy sets and representing

his/her preferences. The ontology -more precisely the taxonomies of values associated with

symbolic types- is used in order to assess which data can be considered as “near” to the user’s selection criteria. A query is asked to the MIEL++ system through a single graphical user interface, which relies on the domain ontology. The query is translated into a query expressed in the query language of each data source: an SQL query in the relational local database (see Buche et al. 2005) for more details about the SQL subsystem), a SPARQL query in the RDF graph base. SPARQL is the querying language recommended by the W3C to query semantic annotations expressed in RDF graphs. Finally, the global answer to the query is the union of the local results of the two subsystems, which are ordered according to their relevance to the query selection criteria. In this paper, we focus on three original aspects of the SPARQL querying: (1) the use of the taxonomies of values associated with symbolic types to enlarge the querying, (2) the way comparisons between the user’s selection criteria and fuzzy annotations are done, (3) the total order defined to retrieve the most pertinent data to the user.

Let us consider a MIEL++ query Q expressed in the relation GrowthParameterAw and having for selection criteria (aw=awPreference) and (Microorganism=MicroPreferences). The continuous fuzzy set awPreferences, which is equal to [0.9, 0.94, 0.97, 0.99], means that the end-user is first interested in aw values in the interval [0.94, 0.97]. But he/she accepts to enlarge the querying till the interval [0.9, 0.99]. The discrete fuzzy set MicroPreferences, which is equal to {1.0/Gram+, 0.5/Gram-}, means that the end-user is interested in micro- organisms which are first Gram+ and then Gram-. This fuzzy set defines implicitly user’s preferences for micro-organisms which are kinds of Gram+ and Gram-. According to the taxonomy of values associated with the symbolic type Microorganism, Clostridium Botulinum and Staphylococcus Spp. are kind of Gram+ and Salmonella is a kind of Gram-. In order to take those implicit preferences into account in the querying, we propose to perform a closure of the fuzzy set MicroPreferences (see Thomopoulos et al. 2006 for more details).

Intuitively, the closure propagates degrees of preferences to more specific values of the taxonomy. By example, the closure of the fuzzy set MicroPreferences is: {1.0/Gram+, 0.5/Gram-, 1.0/Clostridium Botulinum, 1.0/ Staphylococcus Spp., 0.5/Salmonella}.

In order to build the answer, selection criteria representing user’s preferences expressed as fuzzy sets must be compared with fuzzy annotations. But the fuzzy sets used in the annotations have two different semantics. We propose to realise those comparisons separately using two different measures: (i) a possibility degree of matching (noted P) and a necessity degree of matching (noted N) which are classically used (see Dubois et Prade 1988) to compare a fuzzy set having a semantic of preference with a fuzzy set having a semantic of imprecision and (ii) an adequation degree as proposed in (Baziz et al. 2006) to compare a fuzzy set having a semantic of preference with a fuzzy set having a semantic of similarity.

Let (a=v) be a selection attribute of the MIEL++ query Q, v' a fuzzy annotation of the attribute a stored in a RDF graph, sem

the semantic of v', m

and m

their respective membership functions defined on the domain Dom and cl the function which corresponds to the fuzzy set closure. The comparison result depends on the semantic of the fuzzy set v'. If sem

=imprecision, the comparison result is given by the possibility degree of matching between v and v' noted P(v,v')=sup

(min(m

(x), m

(x)) and the necessity degree of matching between v and v' noted N(v,v')=inf

(max(m

(x), 1 - m

(x)). If sem

=similarity, the comparison result is given by the adequation degree between cl(v) and cl(v') noted ad(cl(v), cl(v'))=sup

(min(m

(x), m

(x)).

The comparison results of fuzzy sets having the same semantic (similarity or imprecision) and associated with different selection criteria are aggregated using the min operator. Therefore, an answer to a query is a set of tuples composed of (i) the pertinence score ps associated with the queried relation, (ii) three comparison scores associated with the selection criteria of the query: a global adequation score ad

and two global matching scores P

and N

, and, (iii) the values associated with the projection attribute of the query. Based on those scores, we propose to define a total order on the answers which gives greater importance to the most pertinent answers compared with the ontology: ps, ad

, N

and P

.

The answer to MIEL++ query Q considered on the previous page and compared with the

annotations associated with the first row of Table 1 is given below:

{ps=1, ad

=0.5, N

=1, P

=1, Microorg=(0.5/Clostridium Perfringens+0.5/Clostridium Botulinum), aw=[0.943, 0.95, 0.96, 0.97]},

{ps=1, ad

=0.5, N

=0.5, P

=0.68, Microorg=(0.5/Staphylococcus spp.+0.5/Staphylococcus aureus), aw=[0.88, 0.98, 0.98, 0.99]},

{ps=1, ad

=0.5, N

=0, P

=0.965, Microorg=(1.0/Salmonella), aw=[0.94, 0.99, 0.99, 0.991]}

Results and discussion

In preliminary tests performed on a RDF graph base composed of more than 22000 RDF triples (312 graphs), we have evaluated 5 queries (see Table 2) covering at least 50% of the base entries. Querying quality is assessed using two measures: precision and recall. Precision is the ratio of correct answers over the total number of computed answers. Recall is the ratio of correct computed answers over the number of expected answers. We obtain better results in the queries where the selection criterion concerns micro-organisms than in the ones concerning food products. This is due to the fact that micro-organism names are more standardized in Web tables than food product names. Therefore, the quality of the fuzzy annotations associated with the micro-organism symbolic type is better than with the food product type. Nevertheless, we obtain a precision of 100% for the two last queries concerning food product if we put a threshold of 0.7 on the terms similarity degrees.

Table 2: Evaluation of query results

Queried relation Selection criteria Precision-recall Nb of answer graphs Lag Time Microorganism=L. Monocytogenes 100%-100% 47 graphs

Lag Time Microorganism=P. Fluorescens 100%-100% 29 graphs Growth kinetics Microorganism=E. Coli 100%-100% 39 graphs Lag Time FoodProduct= Egg salad 50%-100% 24 graphs Growth kinetics FoodProduct= Salad 54%-100% 26 graphs

Conclusion

Probabilistic simulations of Sym’Previus software needs a lot of data in food products to take the food matrix into account and to assess food variability in bacterial growth simulations. A prototype of the @WEB and the MIEL++ tools will be soon integrated with the predictive modelling tools of the Sym’Previus project. These automatic links between web data and simulation tools allows a new step in risk assessment to be performed.

References

Baranyi J. and Tamplin M. (2004). ComBase: A Common Database on Microbial Responses to Food Environments. J. Food Prot. 67(9):1834-1840.

Baziz, M., Boughanem, M., Prade, H., Pasi, G. (2006) In: A fuzzy logic approach to information retrieval using a ontology-based representation of documents. in Fuzzy logic and the Semantic Web, Elsevier 363–377

Buche P., Dervin C., Haemmerlé O., Thomopoulos R. (2005) Fuzzy querying of incomplete, imprecise, and heterogeneously structured data in the relational model using ontologies and rules. IEEE Transations on Fuzzy Systems 13(3): 373-383.

Buche P., Dibie-Barthélemy J., Haemmerlé O., Hignette G. (2006) Fuzzy semantic tagging and flexible querying of XML documents extracted from the Web. Journal of Intelligent Information System. 26(1): 25-40

Couvert O., Augustin J.C., Buche P., Carlin F., Coroller L., Denis C., Jamet E., Mettler E., Pinon A., Stahl V., Zuliani V., Thuault D. (2007) Optimising food process and formulation through Sym’Previus, managing of the food safety. Proceedings of 5^th International Conference Predictive Modelling in Foods

Dubois, D., Prade, H. (1988) In: Possibility theory- An approach to computerized processing of uncertainty.

Plenum Press, New York

Hignette G., Buche P., Couvert O., Dibie-Barthélemy J., Doussot D., Haemmerlé O., Mettler E., Soler L. (2008).

Semantic annotation of Web data applied to risk in food. IJFM 128, 174-180.

McMeekin T.A., Baranyi J., Bowman J., Dalgaard P., Kirk M., Ross T., Schmid S., Zwietering M.H. (2006 Information systems in food safety management. Int.J. Food Microbiol. 112:181-194.

Tamplin, M., Baranyi J. and Paoli, G. (2003). Software programs to increase the utility of predictive microbiology information. In: Modelling Microbial responses in Foods. (Eds: R.C McKellar, X. Lu.) CRC, Boca Raton, Fla.

Thomopoulos R., Buche P., Haemmerlé O. (2006) Fuzzy sets defined on a hierarchical domain, IEEE Transactions on Knowledge and Data Engineering 18(10) 1397-1410.

An integrated model for predictive microbiology and simultaneous determination of lag phase duration and exponential growth rate Lihan Huang, Ph.D.

USDA ARS Eastern Regional Research Center, 600 E. Mermaid Lane, Wyndmoor, PA 19038 (lihan.huang@ars.usda.gov)

Abstract

A new mechanistic growth model was developed to describe microbial growth under isothermal conditions. The development of the mathematical model was based on the fundamental phenomenon of microbial growth, which is normally a three-stage process that includes lag, exponential, and stationary phases. A differential logistic growth model was adopted to describe the competitive nature of microbial growth in the exponential and stationary phases. Incorporated with a transitional function to define the lag phase, an integrated differential logistic growth model was developed and solved analytically. The new model was capable of describing a complete three-phase growth curve or a partial growth curve that contains only lag and exponential phases.

The new integrated model was validated using Listeria monocytogenes in tryptic soy broth and beef frankfurters and Escherichia coli O157:H7 in mechanically tenderized beef. The inoculated samples were incubated at various temperature conditions and enumerated to obtain isothermal growth curves. A nonlinear regression procedure in SAS was employed to analyze each growth curve to simultaneously determine the lag phase duration and exponential growth rate. Both bias factor (B

) and accuracy factor (A

) were used to evaluate the performance of the new model.

Results indicated that both B

and A

values were very close to 1.0, suggesting that the new model was very suitable for describing isothermal microbial growth. Modified Ratkowsky models were used to analyze lag phase durations and exponential growth rates and develop secondary models.

The maximum and minimum temperatures obtained from the resulting secondary models matched closely with the biological nature of L. monocytogenes and E. coli O157:H7.

Keywords: growth model, kinetic analysis, mathematical modeling Introduction

The growth of microorganisms in food systems usually exhibits three different phases – lag, exponential, and stationary phases. Several mathematical models have been used in predictive microbiology to describe the microbial growth. These models may include empirical modified Gompertz or logistic model (Gibson et al., 1987), and semi-theoretical Baranyi model (Baranyi et al., 1995). These models can be used to fit the growth curves and obtain the growth parameters, such as lag phase duration and exponential growth rate. Each of these models has both advantages and disadvantages when used to fit growth curves.

The objective of this paper was to report a new integrated kinetic model for quantitative

analysis and characterization of microbial growth under isothermal conditions. The new

model was a theoretical growth model, and was based on the fundamental growth

phenomenon of microorganisms in foods. It clearly defined the duration of lag phase and

exponential growth rate in a single equation, and was more intuitive than the traditional

growth models such as modified Gompertz and Baranyi models.